One can find may examples of how to find the impulse response given a state- space model (A,B,C,D). Is the inverse defined properly i.e given a impulse model can we derive the discrete-time state space model? Is this construction one to one?
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1i presume you mean a discrete-time state space model, not a continuous time state space model? – robert bristow-johnson Oct 25 '19 at 00:26
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you might need some procedure like the prony method to convert your impulse response (as a bandlimited and uniformly-sampled signal) into a sum of decaying exponentials and from that obtain a sum of partial fractions of first and second-order transfer functions, and from that derive poles and zeros. from that can be derived a state-space model.
robert bristow-johnson
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Yes and no.
There, wasn't that easy?
Yes, people do construct models from impulse responses - it's called "system identification".
No, not without outside guidance (as, for instance, an idea of the structure of the system). System identification alone will, at best, give you a transfer function, and even then you often need to make educated guesses about the order of the system (or educated design decisions about the order of the system you're going to assume). System identification alone certainly won't tell you about the physical structure of the system -- it'll just give you a difference equation for the input-output behavior.
TimWescott
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